Steel Designer''''s Manual Part 16 potx

If n is greater than the change value, the plastic neutral axis lies in the tension flange and the formula for higher values of n must be used.. Major axis bending: where Minor axis bend

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where y is the distance to the extreme fibre of the section from the elastic neutral

axis.

For castellated sections, the elastic moduli given are those at the net section The elastic moduli of the tee are calculated at the outer face of the flange and toe of the tee formed at the net section.

For parallel flange channels, the elastic modulus about the minor (y–y) axis is

given at the toe of the section, i.e.

y = B - cy

where B is the width of the section

cy is the distance from the back of the web to the centroidal axis.

For angles, the elastic moduli about both axes are given at the toes of the section, i.e.

yx = A - cx

yy = B - cy

Where A is the leg length perpendicular to the x–x axis

B is the leg length perpendicular to the y–y axis

Cx is the distance from the back of the angle to the centre of gravity,

referred to as the x–x axis

Cy is the distance from the back of the angle to the centre of gravity,

referred to as the y–y axis.

3.2.4 Buckling parameter (u) and torsional index (x)

The buckling parameter and torsional index used in buckling calculations are derived as follows:

(1) For bi-symmetric flanged sections and flanged sections symmetrical about the minor axis only:

u = [ ( 4 Sx2 ) ( A h2 2) ]1 4

1 2g

Z

y

= 1

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where Sx is the plastic modulus about the major axis

Ix is the second moment of area about the major axis

Iy is the second moment of area about the minor axis

A is the cross-sectional area

h is the distance between shear centres of flanges (for T sections, h is the

distance between the shear centre of the flange and the toe of the web)

J is the torsion constant.

3.2.5 Warping constant (H) and torsion constant (J)

(1) I and H sections

The warping constant and torsion constant for I and H sections are calculated

using the formulae given in the SCI publication P057 Design of members subject

(3) Parallel flange channels

For parallel flange channels, the warping constant (H) and torsion constant (J)

are calculated as follows:

ˆ

¯

È Î

1

22

1

2

0 042 0 2204 0 1355 0 0865 0 0725

0 25 2

r T

t r T

t T

1

1 3

1

3 3

33

1 È ÎÍ

-˘

˚˙

I I

y x

Trang 3

where cy= is the distance from the back of the web to the centroidal axis

Note: The formula for the torsion constant (J) is applicable to parallel flange

channels only and does not apply to tapered flange channels.

(4) Angles

For angles, the torsion constant (J) is calculated as follows:

where

(5) ASB sections

torsion constant (J) are as given in Corus brochure, Structural sections.[11]

3.2.6 Plastic modulus (S)

The full plastic moduli about both principal axes are tabulated for all sections except angle sections For angle sections, BS 5950-1: 2000 requires design using the elastic modulus.

The reduced plastic moduli under axial load are tabulated for both principal axes for all sections except asymmetric beams and angle sections For angle sections,

BS 5950-1: 2000 requires design using the elastic modulus.

When a section is loaded to full plasticity by a combination of bending and axial compression about the major axis, the plastic neutral axis shifts and may be located either in the web or in the tension flange (or in the taper part of the flange for a joist) depending on the relative values of bending and axial compression Formulae giving the reduced plastic modulus under combined loading have to be used, which

use a parameter n as follows:

a33

t r T

t T

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For each section, there is a ‘change’ value of n Formulae for reduced plastic modulus

and the ‘change’ value are given below.

(1) Universal beams, universal columns and bearing piles

If the value of n calculated is less than the change value, the plastic neutral axis

is in the web and the formula for lower values of n must be used If n is greater

than the change value, the plastic neutral axis lies in the tension flange and the

formula for higher values of n must be used The same principles apply when

the sections are loaded axially and bent about the minor axis, lower and higher

values of n indicating that the plastic neutral axis lies inside or outside the web

respectively.

Major axis bending:

where

Minor axis bending:

where

(2) Joists

If the value of n calculated is less than the lower change value (n1), the plastic

neutral axis is in the web and the formula for lower values of n must be used.

If n is greater than the higher change value (n2), the plastic neutral axis lies in

4 1

x

2

32

44 4

2 1

Trang 5

the part of the tension flange that is not tapered and the formula for higher

values of n must be used If the value of n calculated lies between the lower change value (n1) and the higher change value (n2), the plastic neutral axis lies

in the tapered part of the flange and then a linear interpolation between the two formulae is used to calculate the reduced plastic modulus.

where

The same principles apply when the sections are loaded axially and bent about

the minor axis, lower and higher values of n indicating that the plastic neutral

axis lies inside or outside the web respectively.

4 1

x

2

32

44 4

2 1 8

q q

Ê Ë

ˆ

¯ 1< < 2

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than the change value, the plastic neutral axis lies in the flange and the formula

for higher values of n must be used.

where

In calculating the reduced plastic modulus of a channel for axial force combined with bending about the minor axis, the axial force is considered as acting at the centroidal axis of the cross-section whereas it is considered to be resisted at the plastic neutral axis The value of the reduced plastic modulus takes account

of the resulting moment due to eccentricity relative to the net centroidal axis.

The reduced plastic modulus of a parallel flange channel bending about the minor axis depends on whether the stresses induced by the axial force and applied moment are the same or of opposite kind towards the back of the channel Where the stresses are of the same kind, an initial increase in axial force may cause a small initial rise of the ‘reduced’ plastic modulus, due to the eccentricity of the axial force.

For each section there is again a change value of n For minor axis bending

the position of the plastic neutral axis when there is no axial load may be either

in the web or in the flanges When the value of n is less than the change value, the formula for lower values of n must be used If n is greater than the change value, the formula for higher values of n must be used.

The formulae concerned are complex and are therefore not quoted here.

The equivalent slenderness coefficient (fa) is tabulated for both equal and unequal angles Two values of the equivalent slenderness coefficient are given for each

unequal angle The larger value is based on the major axis elastic modulus (Zu) to the toe of the short leg and the lower value is based on the major axis elastic modulus to the toe of the long leg.

The equivalent slenderness coefficient (fa) is calculated as follows:

x

2

32

44 4

2 1

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Definitions of all the individual terms are given in BS 5950-1[1], clause B.2.9 The monosymmetry index (ya) is only applicable for unequal angles and is calculated as follows:

Definitions of all the individual terms are given in BS 5950-1[1], Clause B.2.9.

3.3 Hollow sections

Section properties are given for both hot-finished and cold-formed hollow sections The ranges of hot-finished and cold-formed sections covered are different The section ranges listed are in line with sections that are readily available from the major section manufacturers For the same overall dimensions and wall thickness, the section properties for hot-finished and cold-formed sections are different because the corner radii are different.

3.3.1 Common properties

For comment on second moment of area, radius of gyration and elastic modulus, see sections 3.2.1, 3.2.2 and 3.2.3.

For hot-finished square and rectangular hollow sections, the sectional

proper-ties have been calculated, using corner radii of 1.5t externally and 1.0t internally, as

specified by BS EN 10210-2.[9]

For cold-formed square and rectangular hollow sections, the sectional properties

have been calculated, using the external corner radii of 2t if t £ 6 mm, 2.5t if 6 mm

< t £ 10 mm and 3t if t > 10 mm as specified by BS EN 10219–2.[10]The internal corner

radii used are 1.0t if t £ 6 mm, 1.5t if 6 mm < t £ 10 mm and 2t if t > 10 mm, as

2 0 5.

Trang 8

where I is the second moment of area

t is the thickness of section

h is the mean perimeter = 2 [(B - t) + (D - t)] - 2 Rc(4 - p)

Ah is the area enclosed by mean perimeter = (B - t) (D - t) - Rc2(4 - p)

B is the breadth of section

D is the depth of section

Rc is the average of internal and external corner radii.

3.3.3 Torsion modulus constant (C)

For circular hollow sections

For square and rectangular hollow sections

where Z is the elastic modulus and J, t, Ahand h are as defined in section

3.3.2.

3.3.4 Plastic modulus of hollow sections (S)

The full plastic modulus (S) is given in the tables When a member is subject to a

combination of bending and axial load the plastic neutral axis shifts Formulae giving the reduced plastic modulus under combined loading have to be used, which use

the parameter n as defined below.

A is the cross-sectional area

py is the design strength of the steel.

For square and rectangular hollow sections there is a ‘change’ value of n Formulae

for reduced plastic modulus and ‘change’ value are given below.

(1) Circular hollow sections

Sr= S Ê n

Ë

ˆ

¯ cos p 2

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(2) Square and rectangular hollow sections

If the value of n calculated is less than the change value, the plastic neutral axis

is in the webs and the formula for lower values of n must be used If n is greater

than the change value, the plastic neutral axis lies in the flange and the formula

for higher values of n must be used.

where S, Sx , Sy are the full plastic moduli about the relevant axes

4 Bolts and welds

4.1 Bolt capacities

The types of bolts covered are:

• Grades 4.6, 8.8 and 10.9, as specified in BS 4190:[13] ISO metric

black hexagon bolts, screws and nuts.

4395:[14]High strength friction grip bolts and associated nuts and

= - ( ) ( - )

+ È

= - ( ) ( - )

+ È

2

Trang 10

Information on assemblies of matching bolts, nuts and washers is

given is BS 5950-2.[1]

(1) Non-preloaded bolts, Ordinary (Grades 4.6, 8.8 and 10.9) and

HSFG (General and Higher Grade):

(a) The tensile stress area (At) is obtained from the above

standards.

(b) The tension capacity of the bolt is given by:

(c) The shear capacity of the bolt is given by:

As is the shear area of the bolt.

In the tables, Ashas been taken as equal to At.

The shear capacity given in the tables must be reduced for large packings, large grip lengths, kidney shaped slots or long

6.3.2.3 6.3.2.4 6.3.2.5 (d) The effective bearing capacity given is the lesser of the

bearing capacity of the bolt given by:

and the bearing capacity of the connected ply given by:

assuming that the end distance is greater than or equal to

twice the bolt diameter to meet the requirement that Pbs£

0.5 kbsetppbs

tp is the thickness of the ply.

For countersunk bolts, tpis taken as the ply thickness minus half the depth of countersinking Depth of countersinking

is taken as half the bolt diameter based on a 90° countersink 6.3.3.2

Trang 11

e is the end distance

Tables assume standard clearance holes, therefore kbs is

taken as 1.0 For oversize holes and short slots, kbs= 0.7 For

long slots and kidney shaped slots, kbs= 0.5.

(a) The proof load of the bolt (Po) is obtained from BS 4604.[19]

The same proof load is used for countersunk bolts as for non-countersunk bolts For this to be acceptable the head dimensions must be as specified in BS 4933.[20]

1.1 Po for non-slip in service

0.9 Po for non-slip under factored load

PSL= 1.1 KsmPo for non-slip in service

PSL= 0.9 KsmPo for non-slip under factored load where Ks is taken as 1.0 for fasteners in standard

(d) The bearing resistance is only applicable for non-slip in

service and is taken as:

assuming that the end distance is greater than or equal to three times the bolt diameter, to meet the requirement that

Pbg£ 0.5 etppbs.

tp is the thickness of the ply

Trang 12

4.2 Welds

Capacities of longitudinal and transverse fillet welds per unit length

are tabulated The weld capacities are given by:

a is the throat thickness, taken as 0.7 ¥ the leg length

The plates are assumed to be at 90° and therefore K = 1.25

Elec-trode classifications of E35 and E42 are assumed for steel grade S275

and S355 respectively Welding consumables are in accordance with

BS EN 440,[17]BS EN 449,[18]BS EN 756,[19]BS EN 758,[20]or BS EN

References to explanatory notes

1 British Standards Institution

BS 5950 Structural use of steelwork in building.

BS 5950-1: 2000 Code of Practice for design – Rolled and welded sections.

BS 5950-2: 2000 Specification for materials, fabrication and erection: Rolled and

welded sections.

BS EN 10025: 1993 Hot-rolled products of non-alloy structural steels Technical

delivery conditions (including amendment 1995).

BS EN 10113 Hot-rolled products in weldable fine grain structural steels.

BS EN 10113-1: 1993 General delivery conditions (replaces BS 4360: 1990).

BS 4 Structural steel sections.

BS 4-1: 1993 Specification for hot rolled sections (including amendment 2001).

BS EN 10034: 1993 Structural steel I and H sections Tolerances on shape and

dimensions (replaces BS 4-1: 1980).

BS EN 10024: 1995 Hot rolled taper flange I sections Tolerances on shape and

dimensions.

BS EN 10279: 2002 Hot-rolled steel channels Tolerances on shape, dimension

and mass (including amendment 1, amendment 2: 200).

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BS EN 10056 Specification for structural steel equal and unequal angles.

BS EN 10056-1: 1999 Dimensions (replaces BS 4848-4: 1972).

BS EN 10056-2: 1999 Tolerances on shape and dimensions (replaces BS 4848-4:

1972).

BS EN 10210 Hot-finished structural hollow sections of non-alloy and fine grain

structural steels.

BS EN 10210-1: 1994 Technical delivery requirements (replaces BS 4360: 1990).

BS EN 10210-2: 1997 Tolerances, dimensions and sectional properties (replaces

BS 4848-2: 1991).

BS EN 10219 Cold-formed welded structural sections of non-alloy and fine grain

steels.

BS EN 10219-1: 1997 Technical delivery requirements.

BS EN 10219-2: 1997 Tolerances and sectional properties (replaces BS 6363:

1983).

11 Structural sections to BS 4: Part 1: 1963 and BS EN 10056: 1999

Corus Construction and Industrial Sections, 03/2001

12 Nethercot D.A., Salter P.R & Malik A.S (1989)

Design of members subject to combined bending and torsion (SCI-P057)

The Steel Construction Institute, Ascot, Berks.

BS 4190: 2001 ISO metric black hexagon bolts, screws and nuts – Specification.

BS 4395 Specification for high strength friction grip bolts and associated nuts and

washers for structural engineering.

BS 4395-1: 1969 General grade (including amendments 1, amendments 2: 1997).

BS 4395-2: 1969 Higher grade bolts and nuts and general grade washers

(includ-ing amendment 1, amendment 2: 1976).

BS 4604 Specification for the use of high strength friction grip bolts in structural

steelwork Metric series.

BS 4604-1: 1970 General grade (including amendment 1, amendment 2, and

amendment 3: 1982).

BS 4604-2: 1970 – High grade (parallel shank) (including amendment 1,

amend-ment 2: 1972).

BS 4933: 1973 Specification for ISO metric black cup and countersunk head bolts

Trang 14

BS EN 756: 1996 Welding consumables Wire electrodes and wire-flux

combina-tions for submerged arc welding of non-alloy and fine grain steels Classification.

BS EN 758: 1997 Welding consumables Tubular cored electrodes for metal

arc welding with and without a gas shield of non-alloy and fine grain steels Classification.

BS EN 1668: 1997 Welding consumables Rods, wires and deposits for tungsten

inert gas welding of non-alloy and fine grain steels Classification.

Trang 15

Tables of dimensions and gross section properties

Flange Web End Notch Metre Tonne

Trang 17

Trang 19

UNIVERSAL BEAMS

REDUCED PLASTIC MODULUS UNDER AXIAL LOAD

Section Plastic Major Axis Reduced Modulus Plastic Minor Axis Reduced ModulusDesignation Modulus

Lower Values Change Higher Values

ModulusLower Values Change Higher ValuesAxis

Trang 20

UNIVERSAL BEAMS

n =F/(A py), where F is the factored axial load, A is the gross cross sectional area and pyis the design strength of the section

For lower values of n, the reduced plastic modulus, Sr=K1 -K2.n2, for both major and minor axis bending

For higher values of n, the reduced plastic modulus, Sr=K3(1 -n)(K4 +n), for both major and minor axis bending

Trang 21

Trang 23

UNIVERSAL COLUMNS

For lower values of n, the reduced plastic modulus, Sr=K1 -K2.n2, for both major and minor axis bending

For higher values of n, the reduced plastic modulus, Sr=K3(1 -n)(K4 +n), for both major and minor axis bending

Trang 24

DIMENSIONS

Section Mass Depth Width Thickness Radii Depth Ratios for Dimensions for Surface Area

Web Flange Root Toe

between Local Buckling Detailing

Per Per

Trang 26

JOISTS

For values of n lower than n1, the reduced plastic modulus, Srx=Srx1=K1 -K2.n2, for major axis bending

For values of n higher than n2, the reduced plastic modulus, Srx=Srx2=K3(1 -n)(K4 +n), for major axis bending

For values of n between n1and n2, the reduced plastic modulus, Srx=Srx1+(Srx2-Srx1)(n - 1)/(n2- 1), for major axis bending

For lower values of n, the reduced plastic modulus, Sry=K1 -K2.n2, for minor axis bending

For higher values of n, the reduced plastic modulus, Sry=K3(1 -n)(K4 +n), for minor axis bending

Trang 27

Trang 29

UNIVERSAL BEARING PILES

Of n Formula Of n

Axis

Of n Formula Of nx-x

Trang 30

HOT-FINISHED CIRCULAR HOLLOW SECTIONS

DIMENSIONS AND PROPERTIES

Section Mass Area Ratio Second Radius Elastic Plastic Torsional Surface AreaDesignation per of for Moment of Modulus Modulus Constants

Per PerOutside Thickness

Metre Section Local of Area Gyration

Metre TonneDiameter

Buckling

26.9 3.2 1.87 2.38 8.41 1.70 0.846 1.27 1.81 3.41 2.53 0.0845 45.242.4 3.2 3.09 3.94 13.3 7.62 1.39 3.59 4.93 15.2 7.19 0.133 43.048.3 3.2 3.56 4.53 15.1 11.6 1.60 4.80 6.52 23.2 9.59 0.152 42.7

4.0 4.37 5.57 12.1 13.8 1.57 5.70 7.87 27.5 11.4 0.152 34.85.0 5.34 6.80 9.66 16.2 1.54 6.69 9.42 32.3 13.4 0.152 28.560.3 3.2 4.51 5.74 18.8 23.5 2.02 7.78 10.4 46.9 15.6 0.189 41.9

5.0 6.82 8.69 12.1 33.5 1.96 11.1 15.3 67.0 22.2 0.189 27.776.1 2.9 Ÿ 5.24 6.67 26.2 44.7 2.59 11.8 15.5 89.0 23.5 0.239 45.6

3.2 5.75 7.33 23.8 48.8 2.58 12.8 17.0 97.6 25.6 0.239 41.64.0 7.11 9.06 19.0 59.1 2.55 15.5 20.8 118 31.0 0.239 33.65.0 8.77 11.2 15.2 70.9 2.52 18.6 25.3 142 37.3 0.239 27.3

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HOT-FINISHED CIRCULAR HOLLOW SECTIONS

Per PerOutside Thickness

Metre TonneDiameter

406.4 6.3 62.2 79.2 64.5 15900 14.1 780 1010 31700 1560 1.28 20.6

8.0 78.6 100 50.8 19900 14.1 978 1270 39700 1960 1.28 16.310.0 97.8 125 40.6 24500 14.0 1210 1570 49000 2410 1.28 13.112.5 121 155 32.5 30000 13.9 1480 1940 60100 2960 1.28 10.5

457.0 8.0 88.6 113 57.1 28500 15.9 1250 1610 56900 2490 1.44 16.310.0 110 140 45.7 35100 15.8 1540 2000 70200 3070 1.44 13.112.5 137 175 36.6 43100 15.7 1890 2470 86300 3780 1.44 10.5

508.0 8.0 98.6 126 63.5 39300 17.7 1550 2000 78600 3090 1.60 16.210.0 123 156 50.8 48500 17.6 1910 2480 97000 3820 1.60 13.0

16.0 194 247 31.8 74900 17.4 2950 3870 150000 5900 1.60 8.25

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HOT-FINISHED SQUARE HOLLOW SECTIONS

Per PerSize Thickness

6.3 10.3 13.1 6.52 61.6 2.17 20.5 26.0 102 29.6 0.224 21.78.0 12.5 16.0 4.50 69.7 2.09 23.2 30.4 118 33.4 0.219 17.5

70 ¥70 3.6 7.40 9.42 16.4 68.6 2.70 19.6 23.3 108 28.7 0.271 36.6

5.0 9.99 12.7 11.0 88.5 2.64 25.3 30.8 142 36.8 0.267 26.76.3 12.3 15.6 8.11 104 2.58 29.7 36.9 169 42.9 0.264 21.58.0 15.0 19.2 5.75 120 2.50 34.2 43.8 200 49.2 0.259 17.3

80 ¥80 3.6 8.53 10.9 19.2 105 3.11 26.2 31.0 164 38.5 0.311 36.5

4.0 9.41 12.0 17.0 114 3.09 28.6 34.0 180 41.9 0.310 32.95.0 11.6 14.7 13.0 137 3.05 34.2 41.1 217 49.8 0.307 26.66.3 14.2 18.1 9.70 162 2.99 40.5 49.7 262 58.7 0.304 21.48.0 17.5 22.4 7.00 189 2.91 47.3 59.5 312 68.3 0.299 17.1

90 ¥90 3.6 9.66 12.3 22.0 152 3.52 33.8 39.7 237 49.7 0.351 36.3

4.0 10.7 13.6 19.5 166 3.50 37.0 43.6 260 54.2 0.350 32.75.0 13.1 16.7 15.0 200 3.45 44.4 53.0 316 64.8 0.347 26.56.3 16.2 20.7 11.3 238 3.40 53.0 64.3 382 77.0 0.344 21.28.0 20.1 25.6 8.25 281 3.32 62.6 77.6 459 90.5 0.339 16.9

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HOT-FINISHED SQUARE HOLLOW SECTIONS

Per PerSize Thickness

300 ¥300 6.3 57.8 73.6 44.6 10500 12.0 703 809 16100 1040 1.18 20.4

8.0 72.8 92.8 34.5 13100 11.9 875 1010 20200 1290 1.18 16.210.0 90.2 115 27.0 16000 11.8 1070 1250 24800 1580 1.17 13.012.5 112 142 21.0 19400 11.7 1300 1530 30300 1900 1.17 10.516.0 141 179 15.8 23900 11.5 1590 1900 37600 2330 1.16 8.26

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HOT-FINISHED RECTANGULAR HOLLOW SECTIONS

Section Mass Area Ratios for Second Radius of Elastic Plastic Torsional Surface AreaDesignation per of Local Moment Gyration Modulus Modulus Constants

Axis Axis x-x y-y x-x y-y x-x y-y

80 ¥40 3.2 5.62 7.16 22.0 9.50 57.2 18.9 2.83 1.63 14.3 9.46 18.0 11.0 46.2 16.1 0.232 41.3

4.0 6.90 8.79 17.0 7.00 68.2 22.2 2.79 1.59 17.1 11.1 21.8 13.2 55.2 18.9 0.230 33.35.0 8.42 10.7 13.0 5.00 80.3 25.7 2.74 1.55 20.1 12.9 26.1 15.7 65.1 21.9 0.227 27.06.3 10.3 13.1 9.70 3.35 93.3 29.2 2.67 1.49 23.3 14.6 31.1 18.4 75.6 24.8 0.224 21.78.0 12.5 16.0 7.00 2.00 106 32.1 2.58 1.42 26.5 16.1 36.5 21.2 85.8 27.4 0.219 17.5

90 ¥50 3.6 7.40 9.42 22.0 10.9 98.3 38.7 3.23 2.03 21.8 15.5 27.2 18.0 89.4 25.9 0.271 36.6

5.0 9.99 12.7 15.0 7.00 127 49.2 3.16 1.97 28.3 19.7 36.0 23.5 116 32.9 0.267 26.76.3 12.3 15.6 11.3 4.94 150 57.0 3.10 1.91 33.3 22.8 43.2 28.0 138 38.1 0.264 21.5

100 ¥50 3.0 6.71 8.54 30.3 13.7 110 36.8 3.58 2.08 21.9 14.7 27.3 16.8 88.4 25.0 0.292 43.5

3.2 7.13 9.08 28.3 12.6 116 38.8 3.57 2.07 23.2 15.5 28.9 17.7 93.4 26.4 0.292 41.05.0 10.8 13.7 17.0 7.00 167 54.3 3.48 1.99 33.3 21.7 42.6 25.8 135 36.9 0.287 26.66.3 13.3 16.9 12.9 4.94 197 63.0 3.42 1.93 39.4 25.2 51.3 30.8 160 42.9 0.284 21.48.0 16.3 20.8 9.50 3.25 230 71.7 3.33 1.86 46.0 28.7 61.4 36.3 186 48.9 0.279 17.110.0 Ÿ 19.6 24.9 7.00 2.00 259 78.4 3.22 1.77 51.8 31.4 71.2 41.4 209 53.6 0.274 14.0

100 ¥60 3.6 8.53 10.9 24.8 13.7 145 64.8 3.65 2.44 28.9 21.6 35.6 24.9 142 35.6 0.311 36.5

5.0 11.6 14.7 17.0 9.00 189 83.6 3.58 2.38 37.8 27.9 47.4 32.9 188 45.9 0.307 26.56.3 14.2 18.1 12.9 6.52 225 98.1 3.52 2.33 45.0 32.7 57.3 39.5 224 53.8 0.304 21.48.0 17.5 22.4 9.50 4.50 264 113 3.44 2.25 52.8 37.8 68.7 47.1 265 62.2 0.299 17.1

120 ¥60 3.6 9.70 12.3 30.3 13.7 227 76.3 4.30 2.49 37.9 25.4 47.2 28.9 183 43.3 0.351 36.2

5.0 13.1 16.7 21.0 9.00 299 98.8 4.23 2.43 49.9 32.9 63.1 38.4 242 56.0 0.347 26.56.3 16.2 20.7 16.0 6.52 358 116 4.16 2.37 59.7 38.8 76.7 46.3 290 65.9 0.344 21.28.0 20.1 25.6 12.0 4.50 425 135 4.08 2.30 70.8 45.0 92.7 55.4 344 76.6 0.339 16.9

120 ¥80 5.0 14.7 18.7 21.0 13.0 365 193 4.42 3.21 60.9 48.2 74.6 56.1 401 77.9 0.387 26.3

6.3 18.2 23.2 16.0 9.70 440 230 4.36 3.15 73.3 57.6 91.0 68.2 487 92.9 0.384 21.18.0 22.6 28.8 12.0 7.00 525 273 4.27 3.08 87.5 68.1 111 82.6 587 110 0.379 16.810.0 27.4 34.9 9.00 5.00 609 313 4.18 2.99 102 78.1 131 97.3 688 126 0.374 13.6

150 ¥100 5.0 18.6 23.7 27.0 17.0 739 392 5.58 4.07 98.5 78.5 119 90.1 807 127 0.487 26.2

6.3 23.1 29.5 20.8 12.9 898 474 5.52 4.01 120 94.8 147 110 986 153 0.484 21.08.0 28.9 36.8 15.8 9.50 1090 569 5.44 3.94 145 114 180 135 1200 183 0.479 16.610.0 35.3 44.9 12.0 7.00 1280 665 5.34 3.85 171 133 216 161 1430 214 0.474 13.412.5 42.8 54.6 9.00 5.00 1490 763 5.22 3.74 198 153 256 190 1680 246 0.468 10.9

160 ¥80 4.0 14.4 18.4 37.0 17.0 612 207 5.77 3.35 76.5 51.7 94.7 58.3 493 88.0 0.470 32.6

5.0 17.8 22.7 29.0 13.0 744 249 5.72 3.31 93.0 62.3 116 71.1 600 106 0.467 26.26.3 22.2 28.2 22.4 9.70 903 299 5.66 3.26 113 74.8 142 86.8 730 127 0.464 20.98.0 27.6 35.2 17.0 7.00 1090 356 5.57 3.18 136 89.0 175 106 883 151 0.459 16.610.0 33.7 42.9 13.0 5.00 1280 411 5.47 3.10 161 103 209 125 1040 175 0.454 13.5

Check availability in S275

ŸCheck availability in S355

(1)For local buckling calculation d =D -3t and b =B -3t

Trang 35

HOT-FINISHED RECTANGULAR HOLLOW SECTIONS

Section Mass Area Ratios for Second Radius of Elastic Plastic Torsional Surface AreaDesignation per of Local Moment Gyration Modulus Modulus Constants

Axis Axis x-x y-y x-x y-y x-x y-y

200 ¥100 5.0 22.6 28.7 37.0 17.0 1500 505 7.21 4.19 149 101 185 114 1200 172 0.587 26.0

6.3 28.1 35.8 28.7 12.9 1830 613 7.15 4.14 183 123 228 140 1470 208 0.584 20.88.0 35.1 44.8 22.0 9.50 2230 739 7.06 4.06 223 148 282 172 1800 251 0.579 16.510.0 43.1 54.9 17.0 7.00 2660 869 6.96 3.98 266 174 341 206 2160 295 0.574 13.312.5 52.7 67.1 13.0 5.00 3140 1000 6.84 3.87 314 201 408 245 2540 341 0.568 10.8

200 ¥120 5.0 24.1 30.7 37.0 21.0 1690 762 7.40 4.98 168 127 205 144 1650 210 0.627 26.0

6.3 30.1 38.3 28.7 16.0 2070 929 7.34 4.92 207 155 253 177 2030 255 0.624 20.78.0 37.6 48.0 22.0 12.0 2530 1130 7.26 4.85 253 188 313 218 2490 310 0.619 16.510.0 46.3 58.9 17.0 9.00 3030 1340 7.17 4.76 303 223 379 263 3000 367 0.614 13.3

300 ¥100 8.0 47.7 60.8 34.5 9.50 6310 1080 10.2 4.21 420 216 546 245 3070 387 0.779 16.3

10.0 58.8 74.9 27.0 7.00 7610 1280 10.1 4.13 508 255 666 296 3680 458 0.774 13.2

300 ¥200 6.3 47.9 61.0 44.6 28.7 7830 4190 11.3 8.29 522 419 624 472 8480 681 0.984 20.5

8.0 60.3 76.8 34.5 22.0 9720 5180 11.3 8.22 648 518 779 589 10600 840 0.979 16.210.0 74.5 94.9 27.0 17.0 11800 6280 11.2 8.13 788 628 956 721 12900 1020 0.974 13.112.5 91.9 117 21.0 13.0 14300 7540 11.0 8.02 952 754 1170 877 15700 1220 0.968 10.516.0 115 147 15.8 9.50 17400 9110 10.9 7.87 1160 911 1440 1080 19300 1470 0.959 8.34

400 ¥200 8.0 72.8 92.8 47.0 22.0 19600 6660 14.5 8.47 978 666 1200 743 15700 1140 1.18 16.2

10.0 90.2 115 37.0 17.0 23900 8080 14.4 8.39 1200 808 1480 911 19300 1380 1.17 13.012.5 112 142 29.0 13.0 29100 9740 14.3 8.28 1450 974 1810 1110 23400 1660 1.17 10.516.0 141 179 22.0 9.50 35700 11800 14.1 8.13 1790 1180 2260 1370 28900 2010 1.16 8.26

450 ¥250 8.0 85.4 109 53.3 28.3 30100 12100 16.6 10.6 1340 971 1620 1080 27100 1630 1.38 16.2

10.0 106 135 42.0 22.0 36900 14800 16.5 10.5 1640 1190 2000 1330 33300 1990 1.37 12.912.5 131 167 33.0 17.0 45000 18000 16.4 10.4 2000 1440 2460 1630 40700 2410 1.37 10.5

Trang 36

COLD-FORMED CIRCULAR HOLLOW SECTIONS

Section Mass Area Ratio for Second Radius of Elastic Plastic Torsional Surface AreaDesignation per of Local Moment Gyration Modulus Modulus Constants

Diameter

26.9 2.0 ‡ 1.23 1.56 13.5 1.22 0.883 0.907 1.24 2.44 1.81 0.0845 68.72.5 ‡ 1.50 1.92 10.8 1.44 0.867 1.07 1.49 2.88 2.14 0.0845 56.33.0 ‡ 1.77 2.25 8.97 1.63 0.852 1.21 1.72 3.27 2.43 0.0845 47.7

2.5 ‡ 1.92 2.45 13.5 3.00 1.11 1.78 2.44 6.00 3.56 0.106 55.23.0 ‡ 2.27 2.89 11.2 3.44 1.09 2.04 2.84 6.88 4.08 0.106 46.74.0 ‡ 2.93 3.73 8.43 4.19 1.06 2.49 3.55 8.38 4.97 0.106 36.24.5 ‡ 3.24 4.13 7.49 4.50 1.04 2.67 3.87 9.01 5.35 0.106 32.7

3.0 ‡ 2.91 3.71 14.1 7.25 1.40 3.42 4.67 14.5 6.84 0.133 45.73.5 ‡ 3.36 4.28 12.1 8.16 1.38 3.85 5.31 16.3 7.69 0.133 39.64.0 ‡ 3.79 4.83 10.6 8.99 1.36 4.24 5.92 18.0 8.48 0.133 35.1

3.0 ‡ 3.35 4.27 16.1 11.0 1.61 4.55 6.17 22.0 9.11 0.152 45.43.5 ‡ 3.87 4.93 13.8 12.4 1.59 5.15 7.04 24.9 10.3 0.152 39.34.0 ‡ 4.37 5.57 12.1 13.8 1.57 5.70 7.87 27.5 11.4 0.152 34.85.0 ‡ 5.34 6.80 9.66 16.2 1.54 6.69 9.42 32.3 13.4 0.152 28.5

3.0 ‡ 4.24 5.40 20.1 22.2 2.03 7.37 9.86 44.4 14.7 0.189 44.63.5 ‡ 4.90 6.25 17.2 25.3 2.01 8.39 11.3 50.6 16.8 0.189 38.64.0 ‡ 5.55 7.07 15.1 28.2 2.00 9.34 12.7 56.3 18.7 0.189 34.15.0 ‡ 6.82 8.69 12.1 33.5 1.96 11.1 15.3 67.0 22.2 0.189 27.7

Trang 37

‡ Grade S275 not available from some leading producers Check availability.

Trang 38

6.0 ‡ 51.7 65.9 59.3 10100 12.4 566 733 20100 1130 1.12 21.78.0 ‡ 68.6 87.4 44.5 13200 12.3 742 967 26400 1490 1.12 16.310.0 ‡ 85.2 109 35.6 16200 12.2 912 1200 32400 1830 1.12 13.112.0 ‡ 102 130 29.6 19100 12.2 1080 1420 38300 2150 1.12 11.012.5 ‡ 106 135 28.4 19900 12.1 1120 1470 39700 2230 1.12 10.616.0 ‡ 134 171 22.2 24700 12.0 1390 1850 49300 2770 1.12 8.36

8.0 ‡ 78.6 100 50.8 19900 14.1 978 1270 39700 1960 1.28 16.310.0 ‡ 97.8 125 40.6 24500 14.0 1210 1570 49000 2410 1.28 13.112.0 ‡ 117 149 33.9 28900 14.0 1420 1870 57900 2850 1.28 10.912.5 ‡ 121 155 32.5 30000 13.9 1480 1940 60100 2960 1.28 10.616.0 ‡ 154 196 25.4 37400 13.8 1840 2440 74900 3690 1.28 8.31457.0 8.0 ‡ 88.6 113 57.1 28400 15.9 1250 1610 56900 2490 1.44 16.3

10.0 ‡ 110 140 45.7 35100 15.8 1540 2000 70200 3070 1.44 13.112.0 ‡ 132 168 38.1 41600 15.7 1820 2380 83100 3640 1.44 10.912.5 ‡ 137 175 36.6 43100 15.7 1890 2470 86300 3780 1.44 10.516.0 ‡ 174 222 28.6 54000 15.6 2360 3110 108000 4720 1.44 8.28508.0 8.0 ‡ 98.6 126 63.5 39300 17.7 1550 2000 78600 3090 1.60 16.2

10.0 ‡ 123 156 50.8 48500 17.6 1910 2480 97000 3820 1.60 13.012.0 ‡ 147 187 42.3 57500 17.5 2270 2950 115000 4530 1.60 10.912.5 ‡ 153 195 40.6 59800 17.5 2350 3070 120000 4710 1.60 10.516.0 ‡ 194 247 31.8 74900 17.4 2950 3870 150000 5900 1.60 8.25

‡ Grade S275 not available from some leading producers Check availability

Trang 39

COLD-FORMED SQUARE HOLLOW SECTIONS

Size Thickness

Per PerBuckling

30 ¥30 2.0 ‡ 1.68 2.14 10.0 2.72 1.13 1.81 2.21 4.54 2.75 0.113 67.3

2.5 ‡ 2.03 2.59 7.00 3.16 1.10 2.10 2.61 5.40 3.20 0.111 54.73.0 ‡ 2.36 3.01 5.00 3.50 1.08 2.34 2.96 6.15 3.58 0.110 46.6

40 ¥40 2.0 ‡ 2.31 2.94 15.0 6.94 1.54 3.47 4.13 11.3 5.23 0.153 66.2

2.5 ‡ 2.82 3.59 11.0 8.22 1.51 4.11 4.97 13.6 6.21 0.151 53.53.0 ‡ 3.30 4.21 8.33 9.32 1.49 4.66 5.72 15.8 7.07 0.150 45.54.0 ‡ 4.20 5.35 5.00 11.1 1.44 5.54 7.01 19.4 8.48 0.146 34.8

50 ¥50 2.0 ‡ 2.93 3.74 20.0 14.1 1.95 5.66 6.66 22.6 8.51 0.193 65.9

2.5 ‡ 3.60 4.59 15.0 16.9 1.92 6.78 8.07 27.5 10.2 0.191 53.13.0 ‡ 4.25 5.41 11.7 19.5 1.90 7.79 9.39 32.1 11.8 0.190 44.74.0 ‡ 5.45 6.95 7.50 23.7 1.85 9.49 11.7 40.4 14.4 0.186 34.15.0 ‡ 6.56 8.36 5.00 27.0 1.80 10.8 13.7 47.5 16.6 0.183 27.9

60 ¥60 3.0 ‡ 5.19 6.61 15.0 35.1 2.31 11.7 14.0 57.1 17.7 0.230 44.3

4.0 ‡ 6.71 8.55 10.0 43.6 2.26 14.5 17.6 72.6 22.0 0.226 33.75.0 ‡ 8.13 10.4 7.00 50.5 2.21 16.8 20.9 86.4 25.6 0.223 27.4

70 ¥70 2.5 ‡ 5.17 6.59 23.0 49.4 2.74 14.1 16.5 78.5 21.2 0.271 52.4

3.0 ‡ 6.13 7.81 18.3 57.5 2.71 16.4 19.4 92.4 24.7 0.270 44.03.5 ‡ 7.06 8.99 15.0 65.1 2.69 18.6 22.2 106 28.0 0.268 38.04.0 ‡ 7.97 10.1 12.5 72.1 2.67 20.6 24.8 119 31.1 0.266 33.45.0 ‡ 9.70 12.4 9.00 84.6 2.62 24.2 29.6 142 36.7 0.263 27.1

Trang 40

V

COLD-FORMED SQUARE HOLLOW SECTIONS

Size Thickness

Per PerBuckling

300¥300 8.0 ‡ 71.6 91.2 32.5 12800 11.8 853 991 20300 1290 1.17 16.3

10.0 ‡ 88.4 113 25.0 15500 11.7 1030 1210 25000 1570 1.16 13.112.0 ‡ 104 132 20.0 17800 11.6 1180 1400 29500 1830 1.14 11.012.5 ‡ 108 137 19.0 18300 11.6 1220 1450 30600 1890 1.14 10.6

‡ Grade S275 not available from some leading producers Check availability

(1)For local buckling calculation d =D -5t

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